How many positive integral solutions are there for the equation $x + y + z = 3$

15

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55

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10

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1

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Solution

The correct option is D $1$
Given $x + y + z = 3$ $,$ $x, y, z > 0$
Total combinations is given by $^{n - 1} C_{r - 1}$
Here, $n = 3$ $,$ $r = 3$
$\Rightarrow^{3 - 1} C_{3 - 1} =^{2} C_{2} = 1$ i.e. $(1, 1, 1)$
Hence, the answer is $1.$

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